Practical Issues in the Current Expected Credit Loss (CECL) Model: Effective Loan Life and Forward-looking Information

Transcription

1 Practical Issues in the Current Expected Credit Loss (CECL) Model: Effective Loan Life and Forward-looking Information Deming Wu * Office of the Comptroller of the Currency deming.wu@occ.treas.gov December 2016 * Corresponding author, Office of the Comptroller of the Currency, United States Department of the Treasury, 400 7th Street SW, Mail Stop 6E-3, Washington, DC 20219, phone: (202) , fax: (202) , Deming.Wu@occ.treas.gov. The views expressed in this paper are those of the authors, and do not necessarily reflect those of the Office of the Comptroller of the Currency, or the United States Department of the Treasury.

2 Practical Issues in the Current Expected Credit Loss (CECL) Model: Effective Loan Life and Forward-looking Information Abstract We examine the practical issues associated with two important differences between the current incurred loss model and the proposed Current Expected Credit Loss (CECL) Model: the lifetime loss concept and the use of forward-looking information. Our study covers mortgages, auto loans, credit cards, home equity lines of credit (HELOC), and large corporate credits. We find that, because of high attrition rates, the average effective loan life of each loan type is generally below four years, which is substantially shorter than the contractual loan life. We find that the lifetime default rate approximately equals the product of 1-year default rate and the average effective loan life. Compared with 1-year default rates, the levels and volatilities of 5-year cumulative default rates are substantially higher, suggesting that the CECL model could lead to increases in the levels and volatilities of banks loan loss reserves. We employ the discrete-time hazard model as a tractable approach to incorporate forward-looking information in loss forecasting, and find that the forecast errors of 5-year cumulative default rates are substantially higher, even though we allow banks to have perfect foresight in forecasting future economic conditions. JEL classification: G21; G28; M41; M48 Key words: CECL; ALLL; Loss forecast; Effective loan life; Cumulative default rates

3 1. Introduction In the aftermath of the recent global economic crisis, the current incurred loss model of credit loss accounting was criticized for delaying recognition of credit losses until they are probable (or have been incurred). In response to this criticism, the Financial Crisis Advisory Group recommended exploring alternatives to the incurred loss model that would use more forward-looking information (Financial Accounting Standards Board, 2012). In April 2016, the Financial Accounting Standards Board (FASB) voted to implement a new methodology for calculating allowance for loan and lease losses (ALLL) for banks in the United States. Under the proposed current expected credit loss (CECL) model, allowances will be based on the current estimate of all contractual cash flows not expected to be collected. As CECL could bring massive changes to the banks loan loss provisions 1, it is critical to analyze the practical differences between the current incurred loss model and the proposed CECL model. In this study, we examine two important practical issues of the proposed CECL model: the effective life of loans and the use of forward-looking information in loss forecasting. These practical issues arise from the two major differences between the current incurred loss model and the proposed CECL model. The first difference is the lifetime loss concept. Specifically, the proposed CECL model requires banks estimate and reserve for expected losses over the full life of a loan, while the current incurred loss model typically requires banks to reserve for expected losses over the next 12 months. The second difference is the use of forward looking information. More specifically, the probable and incurred thresholds for recognition of credit losses have limited the use of forward-looking information in the incurred loss model. In contrast, the proposed CECL model removes these thresholds and broadens the range of 1 The Q implementation date of CECL applies to public business entities that are SEC filers. For other banks the start date is

4 information that must be considered in measuring the allowance for expected credit losses. Under CECL, the estimate of expected credit losses would be based on historical loss experience, current conditions, and reasonable and supportable forecasts of future economic conditions. One major criticism over the current incurred loss model is the built-in procyclicality of the loss forecasts. Under the incurred loss model, banks forecast credit losses over the next 12- month window. If the credit losses over the next 12 months are highly related to current business cycle conditions, banks may reserve less during boom periods and reserve more during downturn periods. One implication of this procyclicality of loss forecasts is that it could further increase the procyclicality of bank lending. 2 For instance, because banks forecast lower losses during an economic upswing, they will have lower provisions for credit losses. The lower loss provisions, which translate into higher retained earnings and capital, give lenders more incentives to lower underwriting standards and increase lending. Conversely, when the economy is in a downswing, banks will forecast higher losses and reduce lending. Under the proposed CECL model, banks will forecast credit losses over the lifetime of loans. If the lifetime losses of loans are less sensitive to business cycle conditions, banks loss provisions will be less sensitive to business cycle conditions. Accordingly, banks may have less incentive to increase lending during the boom periods and reduce lending during downturn periods. The biggest challenge of CECL centers on the lifetime loss concept for several reasons. First, because of data limitations, it is impractical to estimate the lifetime loss using the contractual life of a loan. For instance, few banks can calculate lifetime losses using the 30-year 2 Bank lending is procyclical for both demand-side and supply-side reasons. For instance, loan demands are lower during economic downturns. At the same time, lenders are also reluctant to lend because the economic perspectives are pessimistic. 2

5 contractual life for 30-year mortgages. For this reason, it is important to estimate the effective life of loans. Specifically, the contractual life of a loan is the age of the loan when it reaches maturity, and the effective life of a loan is the age of a loan when the loan exits a lender's portfolio. Loans can exit a lender's portfolio by defaults, loan repayments (e.g., repayments at maturity or prepayments), or loan sales (e.g., the lender sells loans to another lender). Because of defaults, prepayments, and loan sales, the effective life of a loan can be substantially shorter than its contractual life. In addition, the effective loan life may vary by loan type. For instance, one could argue that 30-year mortgage loans have a longer effective life than short-term commercial loans. Furthermore, the effective life of a loan can vary by economic conditions. For instance, because of prepayments, the effective loan life can be shorter in a falling interest rate environment than in a rising interest rate environment. Therefore, whether the proposed CECL model can mitigate the procyclicality of bank lending depends on whether the effective loan life covers a full business cycle. Specifically, if the effective loan life covers a full business cycle, one can argue that the lifetime losses are less sensitive to current economic conditions. On the other hand, if the effective loan life covers only the upswing or the downswing of a business cycle, it is possible that the lifetime losses are more sensitive to current economic conditions. Because the effective loan life varies by loan types and economic conditions, it is possible that the lifetime losses are sensitive to economic conditions for one type of loans, but are not sensitive to economic conditions for another type of loans. For this reason, whether the CECL model mitigates or exacerbates the procyclicality of bank lending is an empirical question. Consequently, the first objective of this study is to estimate the effective loan life for different types of loans. To achieve this objective, we use several data sources that cover 3

6 mortgages, auto loans, credit cards, home equity lines of credit (HELOC), and large corporate loans. Our data sources include an 11-year panel of consumer credit data from Experian over the period of , a 10-year panel of consumer credit data from Equifax that covers the period of , and an 18-year panel of syndicated corporate credit data from the shared national credit database (SNC) that covers the period of To our knowledge, this study is the first comprehensive study to estimate the effective loan life for different loans over relatively long periods. Overall, we find that attrition rates, or the rates at which loans exit lenders portfolios, are very high in our samples. For instance, approximately 60% of loans exit lenders portfolios within three years since booked. Consequently, the average effective loan life is generally below 4 years, which is substantially shorter than the typical contractual loan life of the loan types that we examine. According to the NBER, there were 11 complete business cycles from 1945 to The average length of a full business cycle is about 69 months, which on average consists an expansion phase of 58 months and a contraction phase of 11 months. Therefore, on average, the effective loan life is unlikely to cover a full business cycle, but is more likely to cover either the upswing or the downswing of a business cycle. Building on the empirical evidence on the effective life of different loans, the second objective of this paper is to examine the one-year and lifetime cumulative default rates of different types of loans. We use the cumulative default rate as the proxy for cumulative credit loss rates for two practical reasons. First, few empirical studies can examine lifetime credit loss rates, as credit loss data over a relatively long period are generally unavailable. Therefore, we use the cumulative default rate as the proxy for cumulative credit loss rates to circumvent the data limitations. Second, because of data limitations and modeling challenges of loss given 4

7 default (LGD), it is quite common for banks to treat LGD as a constant for each collateral type. For this reason, we regard the cumulative default rate as reasonable proxy for cumulative loss rate. While the data limitations in our study are fully acknowledged, our analyses shed valuable insight on the impacts on loan loss reserves and capital when banks shift from the current accounting standards to the new CECL standards. Under the constant hazard assumption, the 1-year and lifetime default rates follow the approximate identity relation: Lifetime default rate (1-year default rate) (Average effective loan life). (1) In practice, the constant hazard assumption is unlikely to hold. Therefore, whether Eq. (1) provides a reasonable approximation to the relationship between 1-year and lifetime default rates is an empirical question. We find that Eq. (1) indeed provides a reasonable approximation. Therefore, this finding lends support to a practical approach to converting 1-year default rates into the lifetime default rates when data limitations prevent direct estimation of lifetime default rates. 3 The third objective of this study is to compare the effects of economic conditions on one-year and lifetime cumulative default rates for different types of loans. The results of our analyses will shed light on the question of whether the lifetime losses of different types of loans are sensitive to economic conditions. One major challenge of the CECL model is the complication of forecast errors and biases stemming from the use of forward-looking information. The FASB proposal did not provide detailed guidance on how banks should use forward-looking information. In practice, forecast 3 It is important to note that this approximate relation also holds between 1-year loss rate and lifetime loss rate under the constant loss rate assumption. 5

8 errors on future economic conditions could complicate the implications of the CECL model. If a bank s forecasts for future economic conditions are overly optimistic during a boom and overly pessimistic during a recession, it could induce big swings in loan loss reserves. In our analyses, we assume that a bank has perfect foresight in predicting future economic conditions. Evidently, this assumption could lead to a bias that favors the CECL model. Nevertheless, one major challenge to loss forecasting is that researchers and practitioners know little about the underlying relationship between economic conditions and bank credit losses. Therefore, despite the assumption of perfect foresight in forecasting economic conditions, banks do not have perfect foresight in forecasting credit losses. Indeed, we find that forecast errors of 5-year cumulative default rates are substantially higher, even if banks have perfect foresight in forecasting future economic conditions. To the best of our knowledge, this study is the first to examine the practical issues associated with the differences between the current incurred loss model and the CECL Model. Our study contributes to the empirical literature that examines the implications of different accounting methods on loan loss provision. Prior empirical studies, which focus on the incurred loss model, have examined how loan loss provision timeliness affects the procyclicality of bank lending and accounting transparency. Specifically, Beatty and Liao (2011) find that under the incurred loss accounting model, banks that delay recognition of loan losses are also more likely to cut lending in the recessionary periods. Bushman and Williams (2012) argue that while forward-looking provisioning could reduce procyclicality, this benefit comes with the cost of reducing accounting transparency. Finally, Beatty and Liao (2014) point out the potential selfselection problem in which banks that choose more timely loss provisioning could also choose to cut less lending in recessions. More specifically, these studies focus on each bank s aggregate 6

9 loan loss provision. As a result, each bank s loan loss provision could be affected by its capital and liquidity conditions, and its risk management practice. In contrast, our study is based on a random sample of loans from different lenders. Consequently, our study focuses on the loan loss experience at the individual loan level. For this reason, our study complements the existing literature by providing empirical evidence from a different angle. The rest of this paper proceeds as follows. Section 2 describes the data and empirical design for incorporating forward-looking information in loss forecasting. Section 3 presents and discusses the estimation results, and Section 4 concludes. 2. Data and Empirical Strategy 2.1. Data The databases used in this study are credit bureau data from Experian and Equifax, and the shared national credit database (SNC). The samples of consumer loans (mortgages, auto loans, credit cards, and home equity line of credit (HELOC)) are obtained from Experian and Equifax. The Experian samples track the performance of loans originated between July 1998 and June 2009 (the observation window ends in 2010). The Equifax samples track the performance of loans originated between July 2004 and June 2014 (the observation window ends in 2015). For consumer loan samples, we define a loan to be in default if payment is 90 days past due or worse. This definition is consistent with both bank practice and the regulatory definition of default under the Basel framework. We focus only first defaults (i.e., the first time that a loan becomes 90 days past due) in our analyses. Consequently, this study does not consider loan cure rates. The sample of corporate loans is from the shared national credit database (SNC). The SNC sample tracks the performance of syndicated corporate credits from 1996 through Loans 7

10 in this sample were originated between 1996 and June A corporate loan is defined to be in default if the loan has a classified rating, which indicates that the loan is in non-accrual or charge-off status, or is considered fully or partially uncollectible. Table 1 provides a summary of the sample periods, sample sizes, sample balances, and loan sizes for the different samples used in this study. Mean and median credit scores are also reported for the retail loan types. Although all of these data samples are used for each of the empirical analyses described below, we will only present the more in-depth empirical results for mortgage loans due to space limitations Relation between 1-year and lifetime default rate Under the constant hazard assumption, 1-year and lifetime default rates follow the discrete compounding relation: T 1 + R= (1 + r), T R= (1 + r) 1, (2) where R denotes the lifetime default rate, r denotes the 1-year default rate, and T denotes the effective loan life. Eq. (2) leads to the following approximate identity relation when r is small: R Tr. (3) Eq. (3) is just Eq. (1) with different notation. As discussed before, the constant hazard assumption is unlikely to hold in practice. Consequently, whether Eq. (1) can reasonably approximate the relation between 1-year and lifetime default rates is an empirical question Incorporating forward-looking information One major challenge of the CECL model is the complication of forecast errors and biases stemming from the use of forward-looking information. Even in the absence of forecast errors 8

11 for future economic conditions, banks still face the challenge of how to incorporate future economic conditions in the forecast of lifetime losses. For instance, to forecast the 5-year cumulative default rate, one would agree that the economic conditions in each of the next five years would affect the cumulative default rate, but it is difficult to determine the contribution of each year s economic conditions to the cumulative default rate. One tractable approach is the discrete-time hazard model, which allows the economic conditions in each future year to affect the conditional default probability in that year. Therefore, the economic conditions in each future year affect the cumulative default rates through their impacts on the conditional default probability in that year. We estimate five different forms of discrete-time hazards: exponential, Gompertz, Weibull, quadratic form, and an unrestricted form that treats loan age as a categorical variable. Let t denote time, i index an individual loan, X it, 1 be a vector of loan-level risk drivers, and Z t be a macroeconomic variable. Let P it be the conditional probability that a loan i defaults at time t, given that it has not defaulted before time t, we specify the five different forms of discrete-time hazard models as below: Exponential: P = + + it, log µ βxit, 1 lzt 1, 1 P it, (4) Gompertz: P = (5) it, log µ a (loan age) it, 1 βxit, 1 lzt 1, 1 P it, Weibull: 9

12 Quadratic form: P = µ + a ( ) + βx + lz (6) it, log log loan age, 1, 1 1, it it t 1 P it,, 2 log Pit = µ + a1 (loan age) + it, 1 a1 (loan age) + it, 1 βx + it, 1 lzt 1, (7) 1 P it, Unrestricted: P = <= + <= + + a I(5 <= loan age<6) + a I(6 <= loan age) + βx + lz. it, log a1 I(0 loan age<1) it, a2 I(1 loan age<2) it, 1 P it, 6 it, 7 it, it, 1 t 1 (8) KY KY Let P, be the cumulative default probability for K years, and Q it, be the cumulative it attrition rate for K years (e.g., caused by loan repayments, refinancing, and loan sales). After estimating the conditional default probability, the cumulative default probability can be estimated as follows: P = P 1Y it, it, P = P + (1 P ) Y(1 Q ) YP 2Y 1Y 1Y 1Y it, it, it, it, it, + 1 P = P + (1 P ) Y(1 Q ) YP 3Y 2Y 2Y 2Y it, it, it, it, it, + 2 P = P + (1 P ) Y(1 Q ) YP 4Y 3Y 3Y 3Y it, it, it, it, it, + 3 P = P + (1 P ) Y(1 Q ) YP. 5Y 4Y 4Y 4Y it, it, it, it, it, + 4 (9) We use different variables to measure economic conditions, such as NBER recession indicators, real and nominal GDP growth rates, the unemployment rate, the interest rate, stock market returns, the housing price index, stock market volatilities, personal income growth, employment growth, and the Fed s senior loan officer opinion survey, among others. For all retail loans, including mortgages, loan-level risk drivers considered include loan age, debt-to-income ratio (DTI), payment-to-income (PTI) ratio, and account delinquency status (e.g., current, day DPD). Obligor-level variables include consumer credit score and total PTI. 10

13 Variable definitions can be found in Table A1 in the Appendix Results Section 3.1 reports the effective loan life and attrition rates for different types of loans. Section 3.2 examines the relationship between 1-year and lifetime default rates. Sections 3.3 and 3.4 examine the conditional and cumulative default rates of mortgages by loan age and calendar year. Lastly, Sections 3.5 through 3.7 discuss the estimation results of discrete-time hazard models for mortgages, forecast errors, and the impacts of future economic conditions on cumulative default rates. As was noted above, due to space limitations, Sections 3.3 through 3.7 only report the results based on the mortgage samples. The results based on other loan types are qualitatively similar, and are available upon request Effective loan life and attrition rates Table 2 reports the effective loan life and attrition rates for different loan types. The most important finding of this table is that the average effective loan life is generally below 3 years. For instance, the mean (median) effective loan life of mortgages is 2.3 (1.7) years for the Experian sample, which covers the period from 1999 to For the Equifax sample, which covers the period from 2005 to 2015, the mean (median) effective life of mortgages is 2.8 (2.3) years. 5 Other types of loans generally have a shorter effective life than mortgages, except for the 4 For brevity, we suppress the definitions of loan- and obligor-level variables used in the commercial discrete-time hazard model analysis, as those results are not reported. However, the variable definitions and results are available upon request. 5 One reason for the difference in the average effective loan life between the Experian and the Equifax samples could be the differences in the interest rate environments between the two 11

14 Equifax HELOC sample, which has a mean effective loan life of 3.1 years. For large corporate loans, the average effective life is below 2 years. The short effective loan life is the consequence of high attrition rates in our samples. As Table 2 shows, the 3-year attrition rates are between 50% and 70% for all samples. In other words, about 60% of the loans exit the lenders portfolios within 3 years since booked. As discussed before, the primary reasons for loan exits are defaults, loan repayments (e.g., repayments at maturity or prepayments), and loan sales (e.g., the lender sells the loan to another lender). Table 2 also shows that nearly 80% of loans exit the sample within 5 years since booked. Table 3 provides further evidence by examining the effective loan life and attrition rates of mortgages by different vintages. Panel A of Table 3 is based on the Experian sample, and Panel B is based on the Equifax sample. While Table 3 shows modest variations in effective loan life and attrition rates across different vintages, these results are very close to those reported in Table 2. The only exceptions are the effective loan life estimates for the 2008 and 2009 vintages of the Experian sample and the 2013 and 2014 vintages of the Equifax sample, which are shortened due to right-censoring of the data. It is important to note that our samples are annual panels. Consequently, we only observe the last year but not the last month before a loan exits the sample. Since a loan could exit the sample any time during a one-year interval, the results reported in Table 2 and Table 3 could underestimate the mean effective loan life by 0 to 12 months. sample periods. It may also be the case that refinancing activity was lower during the crisis period, which would have resulted in longer effective lives in the Equifax sample, which more fully covers that period. 12

15 3.2. The relation between 1-year and lifetime default rates Table 4 examines the relationship between 1-year and lifetime default rates. 6 As discussed in the previous section, the estimated mean effective loan life could be underestimated by 0 to 12 months. To account for this underestimation bias, Table 4 reports two sets of results, the first set of results (i.e., Panel A) does not consider the underestimation bias of mean effective loan life, and the second sets of results (i.e., Panel B) adjusts for the underestimation bias by adding 1 years to the mean effective loan life. Overall, Table 4 shows that Eq. (1) generally provides a reasonable approximation for converting 1-year default rates to lifetime default rates when data limitations prevent estimating lifetime default rates directly. Specifically, the lifetime default rate is approximately 3 times higher than the 1-year default rate. This finding is consistent with Eq. (1), as the average effective loan life is about 3 years. In column D, we calculate the product of 1-year default rate and the average effective loan life. The values in this column are very close to the corresponding values in column C, the observed lifetime default rates. Finally, column E calculates the differences between columns D and C, which shows that the approximation errors are generally small. Most importantly, Panel B shows that our approximations do not underestimate the lifetime default rates after we adjust the mean effective loan life. There is also an economic reason for the relation between 1-year and lifetime default rates. Specifically, there are two approaches to calculating the lifetime loss of a portfolio. The first approach calculates the lifetime loss directly. The second approach calculates the 1-year loss for each year, and accumulates the 1-year loss over the effective loan life. Both approaches would 6 The 1-year default rate in this subsection is defined as the default rate over the next 12 months for the entire pool of loans in banks portfolios as of a given date. That is, this 1-year default rate is not conditional on loan age. 13

16 yield the same number. Therefore, this difference between the existing incurred loss model and the CECL model will not lead to differences in accounting for the lifetime losses of loans, although it may lead to different levels of loan loss reserves in a given year Conditional and cumulative default rates by loan age Panels A and B of Table 5 report the cumulative default rates of mortgages by origination vintage in the Experian and Equifax samples, respectively. These reports are also called static pool analyses. As Table 5 shows, the cumulative default rates in the Equifax sample are substantially higher compared with those in the Experian sample. The primary reason for this significant difference is the contribution of vintages 2005, 2006, 2007, and These vintages have substantially higher cumulative default rates in both samples. However, they are the youngest vintages in the Experian sample but are the oldest vintages in the Equifax sample. For this reason, these vintages were not old enough to contribute to the cumulative default rates over 5 years or longer for the Experian sample. In contrast, these vintages are old enough in the Equifax sample and lead to higher cumulative default rates over 5 years or longer. It is also important to note that there are important differences between the 1-year default rate reported in Table 5 and the 1-year default rate reported in Table 2. More specifically, the 1-year default rate in Table 2 is the unconditional 1-year default rate, and the 1-year default rate reported in Table 5 is conditional on the loan age. To illustrate this difference, let us consider a loan with an age of 2 years old in a given year. If this loan defaults in the next year, it does not contribute the 1-year default rate reported in Table 5, but it does contribute to the unconditional 1-year default rate reported in Table 2. By the same token, the lifetime default rate reported in Table 2 is also different from cumulative default rates reported in Table 5. More specifically, the lifetime default rates reported 14

17 in Table 2 is unconditional on the loan age, and is right censored by the end of the observation window. In contrast, the average cumulative default rates reported in Table 5 are calculated based on the vintages that reach the required age. For instance, the average 5-year cumulative default rate is calculated based on the vintages that are at least 5 years old. Figs. 1 and 2 present the conditional and cumulative default probabilities by loan age for mortgages in the Experian and Equifax samples. The conditional default probability is the probability that a loan defaults at age t, given that it has not defaulted before age t. The cumulative default probability is the probability that a loan defaults before or at age t. Overall, the Equifax sample has both higher conditional and cumulative default probabilities than the Experian sample. For instance, the 5-year cumulative default rate is about 10% in the Equifax sample, and is about 6% in the Experian sample Conditional and cumulative default rates by calendar year Panels A and B of Table 6 report the cumulative default rates of mortgages by calendar year. For each calendar year, the pool of loans includes all vintages that still stay in the pool at that year. Therefore, the cumulative default rates in these panels are the average cumulative default rates for all vintages that stay in the pool in a given year. Consistent with Table 5, the Equifax sample has higher cumulative default rates than the Experian sample. Figs. 3 and 4 plot the cumulative default rates over time for mortgage loans in the Experian and Equifax samples. The pool of mortgages in each year consists of loans from different vintages that remain in the pool in that year. This figure shows that the 5-year cumulative default rates are substantially higher than the 1-year default rates. If we assume that LGD remains constant, this result would suggest the loan reserves under CECL would be substantially higher than under the current incurred loss model for our data sample. 15

18 Fig. 3 also shows that the 4-year and 5-year cumulative default rates pick up substantially in 2005, long before the financial crisis. In contrast, there is little increase in the 1-year default rate in This pattern seems to support the argument that the CECL model will lead to early recognition of credit loss in anticipation of financial distress, if banks can correctly forecast its credit losses in the distant future. 7 In Fig.4, which plots the cumulative default rates for mortgages in the Equifax sample, the 4- year and 5-year cumulative default rates peaked in 2007, immediately before the start of the financial crisis. The 4-year and 5-year cumulative default rates then declined steadily through the crisis period. In contrast, the 1-year default rate peaked in 2008 and stayed high in This comparison again seems to suggest that 4-year and 5-year cumulative default rates exhibit a countercyclical pattern that could mitigate the procyclicality of bank lending, if banks can have reliable forecasts of their future credit losses over long time horizon On the other hand, both Fig. 3 and 4 show the volatilities of cumulative default rates increase with the length of time horizon. Consequently, the high volatilities of cumulative default rates over a longer time window may lead to higher volatilities of bank loan allowances Incorporating forward-looking information with discrete-time hazard models This section examines incorporating forward-looking information with discrete-time hazard models. We estimate five different forms of discrete-time hazard models: exponential, Gompertz, Weibull, quadratic form, and an unrestricted form that treats loan age as a categorical variable. Figs. 5, 6, and 7 compare the predictions of conditional and cumulative default probabilities of 7 Nevertheless, it is debatable whether banks can have reliable forecasts of their credit losses over a long time horizon. For instance, few people could claim that they have correctly forecast the financial crisis. 16

19 these different models. While Fig. 5 shows considerable differences in the predictions of conditional default probabilities of these models, Figs. 6 and 7 show minimal differences in the predictions of cumulative default probabilities for both the Experian and Equifax samples. For this reason and for brevity, we only report the regression results based on the quadratic form hazard model. To measure economic conditions, we considered a broad range of macroeconomic variables, such as NBER recession indicators, real and nominal GDP growth rates, the unemployment rate, the interest rate, stock market returns, the housing price index, stock market volatilities, personal income growth, employment growth, and the Fed s senior loan officer opinion survey, among others. It turns out that state HPI changes, real GDP growth, and the first difference of state unemployment rate have better predictive powers than other macroeconomic variables. Therefore, we only report the regression results based these three macroeconomic variables. We have also tried to included multiple macroeconomic variables in the regression and found it did not improve the model prediction power. Furthermore, multicollinearity is a concern when multiple macroeconomic variables are included in a single regression. For this reason, we only include a single macroeconomic variable in each regression. Table 6 reports the summary statistics of selected variables for the mortgages samples. Table 8 reports the regression results. Panels A and B report the estimation results based on the Experian sample, and Panels C and D report the estimation results based on the Equifax sample. For each sample, two sets of models are estimated, the first set of models use loan information at origination time and the second set of models use updated loan information. Table 8 shows that the coefficient of each macroeconomic variable has the expected sign. For instance, the coefficient of state HPI changes is negative, which is consistent with economic 17

20 theories that suggest rising housing prices reduce mortgage defaults. The coefficient of real GDP growth is also negative, as a booming economy would lead to lower mortgage defaults. Finally, the coefficient of the first difference of state unemployment rate is positive, which is also consistent with economic theories, as rising unemployment rates are typically associated with higher mortgage defaults. A second important finding is that using updated loan information improves model fitting and model prediction. For instance, models that using updated loan information have higher pseudo R 2 and accuracy ratios than models that use loan information at origination. On the other hand, the coefficients of macroeconomic variables are smaller in models using updated loan information, which suggest that using updated loan information could dampen the impacts of macroeconomic variables. A third important finding is the model stability across the Experian and Equifax samples. For instance, the Experian and Equifax samples used different versions of credit scores. The credit score in the Experian sample is Scorex Plus, and the credit score in the Equifax sample is VantageScore 2.0. As Panels A through D show, the coefficients of credit score in all regressions are within a small range between and -0.14, regardless of whether it is Scorex Plus or VantageScore 2.0, and whether models use updated loan information or not Forecast errors on cumulative default rates In this study, we assume that banks have perfect foresight in forecasting future economic conditions with no forecast errors. Understandably, this assumption gives rise to a bias that favors the CECL model in forecast comparisons. Figs. 8 and 9 compare the forecast errors of cumulative default rates over time. For 1-year default rates, the predicted values are reasonably close to their actual values. On the other hand, there are substantial differences between the 18

21 actual and predicted 5-year cumulative default rates, even though we already assume that banks have perfect foresight in forecasting economic conditions. This finding highlights the challenge of implementing CECL: researchers and practitioners know little about the underlying relation between economic conditions and bank credit losses. Moreover, forecasting errors on future economic conditions will lead to further complications in the accuracy predicting lifetime default rates Economic conditions and cumulative default rates Table 9 reports the estimated impacts of changes in economic conditions on the forecasted cumulative default rates of one to five years. We assume that there is a 1% temporary increase in a macroeconomic variable in the year when a bank forecasts the cumulative default rates over the next one to five years. The increase in the macroeconomic variable is temporary, as values of this macroeconomic variable in future periods will be its actual realized values (recall that the bank has perfect foresight in forecasting future economic conditions). Panel A of Table 9 reports the estimated results based on the Experian sample, and Panel B reports the results based on the Equifax sample. As this table shows, the results in both samples are very similar. In addition, the impacts of macroeconomic variables are larger when models do not use updated loan information. For models that are based on the Experian data and use loan information at origination, a 1% increase in state HPI growth would reduce the 1-year default rate by 0.168% (i.e., 16.8 basis points), and a 1% increase in real GDP growth rate would reduce the 1-year default rate by 37.6 basis points. Finally, a 1% increase in the first difference of state unemployment rate would increase the 1-year default rate by 61.1 basis points. The impacts on cumulative default rates over multiple years are slightly lower than that of 19

22 one-year default rate. Further, the impacts decrease slightly as the time horizon increases. However, the differences in the impacts on one-year and multiple-year cumulative default rates are rather small. For instance, a 1% increase in real GDP reduced the 5-year cumulative default rate by 32.5 basis points, only slightly lower than the impact on 1-year default rate. 4. Conclusions This study examines practical issues associated with two important differences between the current incurred loss model and the proposed Current Expected Credit Loss (CECL) Model: the lifetime loss concept and the use of forward-looking information. Our study covers mortgages, auto loans, credit cards, home equity lines of credit (HELOC), and large corporate credits. Overall, we find that the average effective loan life is generally below four years, which is substantially shorter than the contractual loan life. The short effective loan life is the result of high attrition rates in our samples. We also find that the effective loan life depends on the specific data sample and the economic context in which the sample is constructed, which poses potential challenges for banks when choosing the effective loan life for the CECL model. In addition, we find that for each loan type, the lifetime default rate approximately equals the product of 1-year default rate and the average effective loan life. This approximation could be a practical approach to convert 1-year default rates to lifetime default rates when direct estimation is not possible. We also find that the CECL model could lead to increases in both the levels and volatilities of banks loan loss reserves. Finally, we employ the discrete-time hazard model as a tractable approach of incorporating forward-looking information in loss forecasting, as it allows the economic conditions in each future year to affect the cumulative default rates through their impacts on the conditional default 20

23 probability in that year. We find that the forecast errors of 5-year cumulative default rates are substantially higher, even though we already assume banks have perfect foresight in forecasting future economic conditions. References Beatty, A., Liao, S., Do delays in expected loss recognition affect banks' willingness to lend? Journal of Accounting and Economics 52, Beatty, A., Liao, S., Financial accounting in the banking industry: A review of the empirical literature. Journal of Accounting and Economics 58, Bushman, R.M., Williams, C.D., Accounting discretion, loan loss provisioning, and discipline of banks' risk-taking. Journal of Accounting and Economics 54, Financial Accounting Standards Board, Financial instruments-credit losses (subtopic ). Financial Accounting Standards Board,. 21

24 Appendix Table A1 Variable definitions Variable Definition Contractual loan life The contractual life of a loan is the age of the loan when it reaches maturity. Effective loan life The effective life of a loan is the age of a loan when the loan exits a lender's portfolio. A loan can exit a lender's portfolio by defaults, loan repayments (e.g., repayments at maturity or prepayments), or loan sales (e.g., the lender sells the loan to another lender). Default status A consumer loan is defined to be in default if payment is 90 days past due or worse. A corporate loan is defined to be in default if the loan has a classified rating, which indicates that the loan is in nonaccrual or charge-off status, or is considered fully or partially uncollectible. Current status This variable indicates the current status of a non-defaulted loan. The current status can be one of the following values: 1 (current), 30 (30-to-59 days past due), 60 (60-to-89 days past due). The current status is a snapshot measure at June 30 of the current year day delinquency This dummy variable equals 1 if the current status of a non-defaulted loan is 30-to-89 days past due. Homeowner This dummy variable equals 1 if the borrower is a homeowner Credit score For Experian data, the credit score of a borrower is Scorex Plus. For Equifax data, the credit score of a borrower is Vantage score 2.0 Subprime This dummy variable equals 1 if the credit score is below 640 Balance The balance of a loan in U.S. dollars Payment The monthly payment of loan Loan PTI The annualized loan payment to income ratio is the annualized loan payment to the annual state average personal income. Total PTI The annualized total payment to income ratio is the annualized borrower s total payments to annual state average personal income. The borrower s total payments include mortgage payments, auto loan payments, credit card payments, HELOC payments, installed loan payments. Loan age The age of loan in years Real GDP growth rate Real GDP growth rate State HPI change Annual change of state-level housing price indices State unemployment rate (first First difference in state unemployment rate difference) 22

25 Table 1 Sample description The samples of consumer loans (mortgages, auto loans, credit cards, and home equity line of credit (HELOC)) are obtained from Experian and Equifax. The Experian samples track the performance of loans originated between July 1998 and June 2009 (the observation window ends in 2010). The Equifax samples track the performance of loans originated between July 2004 and June 2014 (the observation window ends in 2015). The sample of corporate loans is from the shared national credit database (SNC). The SNC sample tracks the performance of syndicated corporate credits from 1996 through Loans in this sample were originated between 1996 and June Period Loan count Sample balance Loan size Credit score ($thousand) ($ billion) Mean Median Mean Median Mortgages (Experian) ,184 $142.2 $158.9 $ Mortgages (Equifax) ,938 $110.2 $200.4 $ Auto loans (Experian) ,292,323 $15.7 $12.2 $ Auto loans (Equifax) ,291,911 $15.7 $12.1 $ Credit cards (Experian) ,361,195 $7.9 $2.3 $ Credit cards (Equifax) ,970,996 $3.9 $2.0 $ HELOC (Experian) ,415 $19.9 $50.4 $ HELOC (Equifax) ,161 $7.8 $59.7 $ Loan size Sample balance ( $million) ($ billion) Mean Median Corporate credit (SNC) ,599 $14,015 $256.7 $

26 Table 2 Effective loan life and attrition rates for different loan types This table reports the effective loan life and attrition rates for different loan types. The samples of consumer loans (mortgages, auto loans, credit cards, and home equity line of credit (HELOC)) are obtained from Experian and Equifax. The Experian samples track the performance of loans originated between July 1998 and June 2009 (the observation window ends in 2010). The Equifax samples track the performance of loans originated between July 2004 and June 2014 (the observation window ends in 2015). The sample of corporate loans is from the shared national credit database (SNC). The SNC sample tracks the performance of syndicated corporate credits from 1996 through Loans in this sample were originated between 1996 and June P90 denotes the 90 th percentile. Effective loan life Attrition rate Mean Median P90 1 year 3 year 5 year Mortgages (Experian) % 63.5% 80.3% Mortgages (Equifax) % 50.6% 71.7% Auto loans (Experian) % 68.8% 96.7% Auto loans (Equifax) % 61.6% 90.5% Credit cards (Experian) % 70.3% 84.1% Credit cards (Equifax) % 62.0% 76.6% HELOC (Experian) % 72.7% 88.9% HELOC (Equifax) % 51.5% 67.4% Corporate credit (SNC) % 74.0% 92.7% 24

27 Table 3 Effective loan life and attrition rates of mortgages by vintage This table reports the effective loan life and attrition rates of mortgage loans by vintage. The Experian sample tracks the performance of mortgages from 2000 through Loans in this sample were originated between July 1998 and June The Equifax sample tracks the performance of mortgages from 2006 through Loans in this sample were originated between July 2004 and June Panel A: Experian sample of mortgages Loan count Effective loan life Attrition rate Mean Median P90 1 year 3 year 5 year All 895, % 63.5% 80.3% , % 54.7% 86.9% , % 83.2% 94.1% , % 87.8% 94.3% , % 80.4% 88.6% , % 60.5% 74.6% , % 51.6% 67.0% , % 58.5% , % 56.2% , % , % , Panel B: Equifax sample of mortgages Effective loan life Attrition rate Loan count Mean Median P90 1 year 3 year 5 year All 549, % 50.6% 71.7% , % 54.0% 68.9% , % 48.2% 67.8% , % 54.3% 72.0% , % 53.8% 76.0% , % 50.6% 76.7% , % 50.0% , % 43.5% , % , % ,

28 Table 4 Relationship between 1-year and lifetime default rates This table reports the approximate identity relationship between the lifetime default rate and the product of the 1-year default rate and the mean effective loan life for different loan types. The results in Panel A do not account for the underestimation bias of mean effective loan life, and the results in Panel B account for the underestimation bias by increasing the mean effective loan life by 1 year. The samples of consumer loans (mortgages, auto loans, credit cards, and home equity line of credit (HELOC)) are obtained from Experian and Equifax. The Experian samples track the performance of loans originated between July 1998 and June 2009 (the observation window ends in 2010). The Equifax samples track the performance of loans originated between July 2004 and June 2014 (the observation window ends in 2015). The sample of corporate loans is from the shared national credit database (SNC). The SNC sample tracks the performance of syndicated corporate credits from 1996 through Loans in this sample were originated between 1996 and June Panel A: Without adjustments on mean effective loan life Mean effective loan life 1-year default rate Lifetime default rate Approximation error A B C D=A*B E=D-C Mortgages (Experian) % 4.80% 4.83% 0.03% Mortgages (Equifax) % 9.70% 8.40% -1.30% Auto loans (Experian) % 5.50% 5.00% -0.50% Auto loans (Equifax) % 8.30% 6.40% -1.90% Credit cards (Experian) % 13.70% 13.00% -0.70% Credit cards (Equifax) % 19.70% 16.79% -2.91% HELOC (Experian) % 3.90% 3.42% -0.48% HELOC (Equifax) % 7.50% 6.51% -0.99% Corporate credit (SNC) % 6.90% 6.27% -0.63% Panel B: With conservative adjustments on mean effective loan life Mean effective loan life 1-year default rate Lifetime default rate Approximation error A B C D=A*B E=D-C Mortgages (Experian) % 4.80% 6.93% 2.13% Mortgages (Equifax) % 9.70% 11.40% 1.70% Auto loans (Experian) % 5.50% 7.50% 2.00% Auto loans (Equifax) % 8.30% 9.60% 1.30% Credit cards (Experian) % 13.70% 19.50% 5.80% Credit cards (Equifax) % 19.70% 24.09% 4.39% HELOC (Experian) % 3.90% 5.22% 1.32% HELOC (Equifax) % 7.50% 8.61% 1.11% Corporate credit (SNC) % 6.90% 9.57% 2.67% 26